Problem: Rewrite as a simplified fraction. ${3.6\overline{7} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 367.7777...\\ 10x &= 36.7777...\end{align*}}$ Subtracting the two equations, we have: ${90x = 331}$ ${x = \dfrac{331}{90}} \text{or} {3 \dfrac{61}{90}}$